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" Hence, any term may be found by adding the product of the common difference by the number of terms less one, to the first term. "
An Introduction to Algebra: Upon the Inductive Method of Instruction - Page 229
by Warren Colburn - 1837 - 276 pages
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An Introduction to Algebra: With Notes and Observations: Designed for the ...

John Bonnycastle - Algebra - 1811 - 220 pages
...III. The last term of any arithmetical series is equal to the sum or difference of the first term, and the product of the common difference by the number of terms less , one ; according as the series is increasing or decreasing. Thus, the 20th term of 2, 4, 6, 8, 10, 12, &c....
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A Treatise on Algebra, in Practice and Theory: With Notes and Illustrations ...

John Bonnycastle - Algebra - 1813
...2 x (a+2d). 5. The last term of any increasing arithmetical series is equal to the first term plus the product of the common difference by the number of terms less one ; and if the series be decreasing, it will he equal to the first term minus that product. Thus, the...
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An Introduction to Algebra: With Notes and Observations : Designed for the ...

John Bonnycastle - Algebra - 1818 - 260 pages
...Or, the sum of any increasing arithmetical series may be found, without considering the last term, by adding the product of the common difference by the number of terms less one to twice the first term, and then multiplying the result by half the number of terms. And, if the series...
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An Introduction to Algebra: With Notes and Observations : Designed for the ...

John Bonnycastle - Algebra - 1818 - 260 pages
...(a+4d)=(a+d)+(a+3d)=2 X(o+2i). 5. The last term of any increasing arithmetical series is equal to the first term plus the product of the common difference by the number of terms less one ; and if the series be decreasing, it will be equal to the first term minus that product. Thus, the...
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The Complete Practical Arithmetician: Containing Several New and Useful ...

Thomas Keith - Arithmetic - 1822 - 332 pages
...13- &c- be 'n arithmetical progression, then will 4. The difference between the extremes is equal to the product of the common difference by the number of terms less one> Thus, if 3. 5. 7. 9. &c. be in arithmetical progression, Tlien will 9—3=2x4—15. The number of terms,...
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The Arithmetical Expositor, Or, A Treatise on the Theory and ..., Volume 1

Enoch Lewis - Arithmetic - 1824
...subsequent term, it is manifest that the whole sum, by which the first term is increased or diminished, is the product of the common difference by the number of terms less one. (48.) The sum of the extremes is evidently equal to the sum of the second from thebeginning, and the...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - Algebra - 1824 - 516 pages
...the terms. Hence the last term of any arithmetical series is equal to the. first term plus or minus, the product of the common difference, by the number of terms less one. 469. Also, if s be put equal to the sum of any number of terms of this progression, we shall have And...
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An Elementary Treatise on Algebra, Theoretical and Practical ...

James Ryan - Algebra - 1824 - 516 pages
...the terms. Hence the last term of any arithmetical series is equal to the first term plus or minus, the product of the common difference, by the number of terms less one. 469. Also, if s be put equal to the sum of any number of terms of this progression, we shaU have And...
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An Introduction to Algebra: With Notes and Observations, Designed for the ...

John Bonnycastle - Algebra - 1825 - 312 pages
...-:d)= x (a+td.) 5. The last term of any increasing arithmetical series is equal to the first term plus the product of the common difference by the number of terms less one ; and it ^ the series be decreasing, it will be equal to the first term minus that product. Thus, the...
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An Introduction to Algebra Upon the Inductive Method of Instruction

Warren Colburn - Algebra - 1828 - 276 pages
...term, r the common difference, and n the number of terms. The series is , a -f- r, a -f- 2 r, a -f- 3 r . . . . a -f- (n — 2) r, a -\- (n — 1) r....series 3, 5, 7, 9, &c. In this a = 3, r = 2, and n — 1 =9. 1 = 3 + 9 X2 = 21. In a decreasing series, r is negative. .? Example. What is the 13th term...
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